Squeezed Gravitons and One-Loop Self-Energy under Light-Cone Smearing

We investigate light-cone smearing induced by quantum fluctuations of gravitons and its implications for the ultraviolet structure of quantum field theory. By treating the first-order correction to Synge's world function as an operator, we show that the retarded Green's function is smeared by the variance of graviton fluctuations. The smearing width depends on the quantum state of gravitons: vacuum fluctuations generate a Gaussian smearing of the light cone, coherent states shift the light-cone position, and squeezed states modify the smearing width itself. We then apply the smeared Feynman propagator to one-loop self-energies in interacting scalar field theories. In both the $\phi^3$ bubble diagram and the $\phi^4$ tadpole diagram, the short-distance singularities responsible for the usual ultraviolet divergences are regularized by a nonzero smearing width. We also estimate the contribution from primordial gravitons generated during inflation and show that it induces a finite correction of order $10^{-10}$ to the one-loop self-energy. Our results suggest that the quantum state of gravitons can leave a finite imprint on the causal and short-distance structure of quantum field theory.